The league leaders played out a 0-0 draw with their great rivals, a result that saw them reclaim their place at the top of the table by a single point from Manchester City.
But it leaves Klopp’s side with no margin for error as they seek to cling to their slender advantage in the race to become Premier League champions.
Firmino was forced off shortly before the break after picking up an ankle injury, and his replacement Daniel Sturridge failed to sufficiently trouble the home side’s defence as the game petered into a stalemate.
Speaking to Sky Sports afterwards, Klopp said: "It was a strange game. We started really well. All the injuries in the game obviously cost us rhythm.
“It happened to us with Bobby [Firmino] and that was a catastrophe.”
In a first half badly disrupted by injuries to both sides, United lost Ander Herrera, Juan Mata and Jesse Lingard to knocks before the break, forcing manager Ole Gunnar Solskjaer to make all three substitutions before half-time.
Lingard had himself only been brought on to replace Mata, but left the field just 17 minutes later as the hosts saw their game-plan torn up by poor fortune.
"United played with a completely new midfield and three up front,” said Klopp. “We lost our rhythm and couldn't get it back.
"It was a game without a lot of highlights - it was intense. On days when United are beatable you have to do it and we didn't do it.”
It was a game of few chances at Old Trafford, with the league leaders frustrated by the hosts despite largely dominating with the ball.
But with the Reds’ lead now slashed from the generous seven-point cushion they had enjoyed in January, Klopp chose to look on the bright side of things ahead of Wednesday’s game against Watford.
"We have a point more and Wednesday is our next game,” the manager said.
"We might feel like we won a point or lost two. We started exactly how we wanted to start.
"We were without chances - only United had one big one when Alisson made an excellent save - the rest were set-pieces. It kept the game open but we didn't create enough and that's the truth.
"We didn't do well to be honest. We take that. It is a point gained because we have one more than before but it doesn't feel like that.”